Mathematical Sciences: Statistical Theory for Classification

数学科学：分类统计理论

• 批准号: 9102867
• 负责人: John Hartigan
• 金额: $ 18.95万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-15 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102867&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistical; Theory; Classification

Probability models can be used to distinguish naturally occurring clusters of observations even when these observations are intermixed and unlabelled. Established theory draws on mixture models, modal models, and, for evolutionary classification, generalized Markov models. This research introduces and investigates a new class of probability models: product partition models. These will have wide application in determining classifications and in predicting based on partial or complete classifications. Applications for these classification algorithms include the construction of evolutionary trees, recognition of change-points for modelled processes, image reconstruction, and failure prediction for complex cases like the space shuttle.

概率模型可用于区分自然发生的观察簇，即使这些观察是混合且未标记的。 既定理论借鉴了混合模型、模态模型，以及用于进化分类的广义马尔可夫模型。 本研究介绍并研究了一类新的概率模型：产品划分模型。 这些将在确定分类和基于部分或完整分类的预测中具有广泛的应用。 这些分类算法的应用包括构建进化树、识别建模过程的变化点、图像重建以及航天飞机等复杂情况的故障预测。